Digital security information embedded in digital content, called watermarking, has many applications, including authentication, copyright protection, copy protection, fingerprinting, and broadcasting channel tracking. Among them, copy protection is one of the most desired applications for watermarking technology. Copy protection should not be confused with copyright protection because, for the former, one key is given to all recipients, while for copyright protection; each image has its own key.
In a symmetric watermarking system, the key used to embed a watermark and the key used to extract a watermark are identical and are kept confidential. This common secret key is a random sequence, which is embedded in a digital image by the spreading spectrum technique. Notable security problems of the symmetric watermarking approach raised from the need of disclosing the secret key to owners and legitimate recipients, as well as from the need to identify the image file that a particular secret key is associated with, especially when the image file belongs to a large image database. This gives invaders a chance to understand content of the secret key. Another problem came from the application side. The watermark serves as evidence of ownership. For attackers, may easily follow the why how the watermark is embedded to remove a forged watermark from the file, whereby the embedded watermark can not be detected using the secret key.
In order to solve these problems, a “zero-knowledge watermark detection” technology was proposed. The basic idea of zero-knowledge watermark detection is to replace the watermark detection process with a cryptographic protocol. Although this approach shows promise, it requires a great deal of bidirectional communications between owners and verifiers to prove ownership of copyright.
Asymmetric watermarking is another approach to solve the above-mentioned problems. An asymmetric watermarking system uses two sets of keys: one for embedding, and the other for detection. The detecting key is made available to the public so that anyone may access to it and is permitted to use it to verify particular watermark from a digital image. The public key of each watermarked image is usually stored in a safe place where a trusted third party can verify its integrity to avoid that anyone could produce a valid public key by one's own asymmetric watermarking method. The public key is open and is easy to verify and to authenticate. In the asymmetric system, the secret embedding keys are not used for verification. Therefore, no secret information is transmitted over the channel, nor can it be accessed in the database.
One important feature of the asymmetric system rests in that it is almost impossible, or at least computationally impossible, for those who know the entire system, except for the secret key, to successfully hack into the system. Some interesting asymmetric schemes have been proposed for watermarking. However, till 2003, researchers still believed that asymmetric watermarking systems suited for commercial use could not exist. See T. Furon and P. Duhamel, “An asymmetric watermarking method,” IEEE Trans. Signal Processing, vol. 51, no. 4, pp. 981-995, April 2003. The asymmetric watermarking methods ever proposed were for copy protection purposes and their watermark detector must be embedded into detection devices, so that inverting the embedding process becomes computationally difficult.
A closest point attack (or projection attack when the detection method is linear) tries to find the forged image that is closest to the watermarked image and this forged image does not detect any watermark. After the projection attack, an image that does not contain the embedded watermark, or contains residual information from where the embedded watermark may not be detected, will be obtained. In the conventional art, there is no watermarking technology that is resistant to closest point attack.